Recently it has been suggested that long range magnetic dipolar interactions are responsible for spin ice behavior in the Ising pyrochlore magnets ${ \rm Dy_{ 2}Ti_{ 2}O_{ 7}}$ and ${ \rm Ho_{ 2}Ti_{ 2}O_{ 7}}$. We report here numerical results on the low temperature properties of the dipolar spin ice model, obtained via a new loop algorithm which greatly improves the dynamics at low temperature. We recover the previously reported missing entropy in this model, and find a first order transition to a long range ordered phase with zero total magnetization at very low temperature. We discuss the relevance of these results to ${ \rm Dy_{ 2}Ti_{ 2}O_{ 7}}$ and ${ \rm Ho_{ 2}Ti_{ 2}O_{ 7}}$.
Categories: cond-mat.dis-nn